Efficient inference for gaussian random field and its applications

Abstract

We address two types of questions in this research: to infer unknown function values of interest with partial and noisy observations, and to decide the location of the next observation, which maximizes the information gain in terms of optimization. Particularly, unknown functions are modeled by Gaussian processes given certain conditions, usually a set of latent variables. This framework is applied into i) 3D reconstruction with cross-sectional 2D images by Piecewise-smooth Markov Random Field

ii) feasibility determination of correlated systems for constrained optimization

and iii) machine learning model selection by estimating their learning curves, which are possibly correlated. The proposed models for each problem show that i) the models have enough expressiveness power, which overcome the limitation of plain Gaussian models

ii) the corresponding inference can be done in an efficient manner

and iii) the sequential decisions based on the models show the superior performance than existing methods.